NUCLEAR-MAGNETIC-RESONANCE RELAXATION ENHANCEMENTS PRODUCED BY PARAMAGNETIC SOLUTES - EFFECTS OF RHOMBICITY IN THE ZERO-FIELD SPLITTING TENSOR WITH THE S=2 SPIN SYSTEM AS AN EXAMPLE

Effects due to the nonuniaxial part of the zero field splitting (ZFS) tensor on NMR relaxation enhancements produced by paramagnetic species in solution (the NMR PRE) has been studied theoretically and experime ntally in the ZFS limit, i.e., in the limit where the ZFS energy is la rge compared to the Zeeman energy. In the ZFS limit, the precessional motion of the electron spin is quantized with respect to molecule-fixe d coordinate axes. The uniaxial part of the ZFS tensor induces precess ional motion in the transverse (xy) components of the electron spin ve ctor S, and xy anisotropy in the ZFS tensor (i.e., a nonzero ZFS param eter E) induces precessional motion in the z component of S. The NMR-P RE phenomenon is particularly sensitive to the motion of S(z) and henc e also to ZFS anisotropy in the xy plane. Mathematical expressions hav e been derived which describe the motion of the spin vector evolving u nder the influence of a general rhombic ZFS Hamiltonian and the influe nce of this motion on the NMR PRE in the ZFS limit. It is shown that o scillations in S(z) occur at the transition frequencies of the S spin system; the frequencies and amplitudes of the precessional components of S(z) can be calculated by diagonalizing the general ZFS Hamiltonian . These motions and their consequences with respect to the behavior of the NMR PRE are described in detail for the S = 2 spin system. A para metrization of NMR-PRE data is proposed which gives a clear criterion for the conditions under which rhombic parts of the ZFS tensor signifi cantly affect the relaxation enhancements produced by an S = 2 spin sy stem. This criterion is of considerable practical importance for the a nalysis of NMR-PRE data, since it defines conditions under which data may be analyzed without the need for independent experimental informat ion concerning the magnitude of the ZFS tensor.